Image Processing Reference
In-Depth Information
Fig. 16.4. Three classes ( white ) that have to be reassigned to a neighbor class ( colored )
can be reassigned in one pass, whereas multipasses are needed if the insignificant
classes are touching each other. First, one can reassign the isolated classes, like those
(a) in Fig. 16.4, by generating a set of candidate classes obtained from the neighbor-
ing classes. This is determined for each pixel of the region. If a label in the
N 8 ( r k )
neighborhood of a point of such a region is different from Γ ( r k ,L ), then a new can-
didate class is obtained. Otherwise, a different point (outside of
N 8 ( r k ), but in the
same direction) is examined until their corresponding class labels differ. These op-
erations are repeated for the eight possible directions of the
N 8 ( r k ). For each pixel
r k , the Euclidean distances between the feature vector prototype of the region, e.g.,
that of (a), and the prototypes of the candidate classes are computed. Each pixel is
then assigned to the closest candidate class. To extend the search outside of the mask
is necessary because not all points share boundaries with a point of a different class.
This can be illustrated by region (a) in Fig. 16.4, where the central pixel near the bor-
der of the image lacks neighbors belonging to significant classes. For these pixels,
an extended search beyond the
N 8 ( r k ) neighborhood is necessary to obtain relevant
candidate classes.
Next, the remaining insignificant classes consisting of touching regions need to
be reassigned. However, the reassignment order leads to different results, and mul-
tipasses are needed to avoid this problem. The process can be illustrated by con-
sidering the classes (b) and (c) in the figure. In the first pass, these two classes are
temporarily reassigned as if they were isolated insignificant classes. The same initial
state of Γ ( r k ,L ) is used for both classes. The maximum number of pixels K n max
reassigned to the same candidate class is determined for each class label γ n equaling
to the class of (b), and ditto for class (c). Then a quotient q n between K n
and
max
the respective population K n of the classes is computed, i.e., q n = K n
/K n .
A value of q n =1means that the class n tends to be reassigned to a single candi-
date class. The reassignment of the region with the largest quotient q n is then taken
first. Suppose that (b) is reassigned first. Before reassigning (c) in a second pass, one
needs to check if (c) is still considered as an insignificant class. It might occur that
pixels of (b) were reassigned to (c), making it a significant class. If this is not the
case, (c) is reassigned using the procedure described for isolated classes. A similar
procedure can be applied to reassign more than two touching insignificant classes,
max
 
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